1. Field of the Invention
The present invention relates to a waveform equalizer for removing signal distortion which arises when a digital signal is recorded and subsequently reproduced, or is transmitted and subsequently received, and to a method of designing such a waveform equalizer. In particular, the invention relates to a waveform equalizer which is formed as a neural network having fixed weighting coefficients.
2. Description of the Related Art
In recent years, systems which utilize recording and playback or transmission/receiving of digital signals have come to be widely utilized. However in such a system, even if an original digital signal which is recorded or transmitted has a substantially ideal digital waveform, the resultant signal that is subsequently produced from a playback apparatus or a receiving apparatus will have a waveform that is very different from such an ideal digital signal waveform, and must be regarded as an analog signal for the purposes of signal processing. The following description will be directed to a digital signal recording and playback system, however similar considerations apply to a digital signal transmission and receiving system. The general term "digital signal transfer system" as used in the following description and in the appended claims is intended to designate a system such as a magnetic or optical recording and playback system, or a digital signal transmission system, in which an original signal is recorded and reproduced to obtain a corresponding distorted digital signal, or is transmitted and received, to obtain a corresponding distorted digital signal.
In the specific case of a digital data magnetic recording and playback system, a phenomenon known as "peak shift" occurs whereby portions of the playback digital signal waveform are shifted in time with respect to other portions of the waveform, as a result of the recording and playback process, thereby causing distortion of the signal and resulting in errors in judging the 0 and 1 logic level states of the playback signal data. In the case of an optical recording and playback system too, signal distortion (intersymbolic interference) arises due to such factors as lens aberration, etc. as described in detail hereinafter.
To overcome such problems, a type of waveform equalizer has been used in the prior art which is based on a transversal filter, as illustrated in the circuit diagram of FIG. 1. The waveform equalizer is assumed to receive as input signal a distorted digital signal produced from a recording and playback system. The output signal from the playback apparatus is delayed by successive identical amounts in delay lines 130a to 130d respectively. The directly supplied input signal and the delayed input signal outputs produced from the delay lines are amplified by amplifiers 131a to 131d respectively, which have predetermined respectively different amplification factors. The resultant amplified output signals are then summed by the adder circuit 132, to obtain a waveform-equalized output signal. However such a waveform equalizer apparatus does not provide satisfactory results.
The digital signal distortion which arises in a magnetic recording and playback system will be described in the following. Diagrams (A) to (E) of FIG. 2 are waveform diagrams for illustrating how such distortion occurs in a magnetic recording and playback system. It is assumed here that NRZ (Non Return to Zero) code is recorded and played back, and that the original recording current signal has an ideal digital waveform, i.e. with rapid transitions between fixed 0 and 1 state digital levels as illustrated in diagram (A). However the magnetic pattern that is actually recorded will be of the form shown in diagram (B). At the time of playback, assuming that such an ideal current waveform has been recorded, then since during playback (if there were no distortion in the record/playback process) the waveform of the output signal from the playback apparatus is differentiated, the resultant waveform would be as shown in diagram (C) of FIG. 2. In this case there is no waveform distortion, and no peak shift has occurred.
However in practice, as shown in diagram (D) of FIG. 2, the playback signal that is actually obtained in this case will be substantially distorted. When such a playback signal is differentiated, then it is found an amount of peak shift such as the amount .DELTA.t has occurred in the differentiated waveform, as shown in diagram (E). Here, a peak value in the differentiated playback signal which should correspond to a recording signal level transition at point t2 of the original recording signal has been displaced. That is to say, for some portions of the playback signal waveform, peak values of the differentiated playback signal will be time-displaced from the correct positions of these peak values. In the NRZ code, one bit is represented by a magnetic polarity inversion. However as a result of such distortion, the positions of inversions of the playback signal waveform will not be clear, so that satisfactory waveform reproduction cannot be achieved. That is to say, although polarity inversions have occurred at the time points t2 and t3, it will be judged (by a circuit which converts the differentiated playback signal of diagram (E) to a data stream) that magnetic polarity inversions have occurred at the time points t1 and t4, or (due to the fact that the signal level at these portions is low) it may be judged that no polarity inversions have occurred in the region from t1 to t4. Conversely, it may be erroneously judged that polarity inversions have occurred at some low-amplitude portions of the playback signal, for example it may be mistakenly judged that inversion has occurred at the time points t5 or t7.
Moreover in the case of an optical type of recording and playback apparatus, even greater degrees of signal distortion can arise. In an optical recording and playback system, defocussing or lens aberration may occur in the optical system of an optical pickup which focusses a small spot of light on the optical disk, and this is a source of overall signal distortion (intersymbolic interference). There are 5 basic types of aberration, and of these, astigmatism, spherical aberration, and coma aberration will result in distortion and intersymbolic interference in the digital signal. In addition, optical aberration can arise as a result of an optical disk being tilted, and this can also result in intersymbolic interference.
Diagrams (A) to (D) of FIG. 3 illustrate how signal distortion can arise in an optical recording and playback system. Here, Tmin designates a minimum duration for which the recorded data remains continuously at the digital 1 or 0 state. In a standard audio signal CD (compact disk) digital recording/playback system, the data that are actually recorded on the disk (i.e. as elongated surface pits, of varying length) represent data that are referred to as "channel bits", which are synchronized with a clock signal known as the channel clock signal, having a frequency of approximately 4.32 MHz. In the field of CD techology the period of that channel clock signal is commonly referred to simply as T, and that designation will be used in the following. The minimum interval between successive inversions of that recorded data will be designated as Tmin. In standard CD operation, the value of Tmin is three periods of the channel clock signal, i.e. 3 T, as illustrated by FIG. 4. However for the purposes of obtaining suitably distorted digital signals to be used in a neural network learning operation as described hereinafter, CDs may be utilized in which the recorded data has a value of Tmin that is less than 3 T.
In diagram (B) of FIG. 3, t1, t2, t3 and t4 denote respective time points which are defined by a the aforementioned channel clock signal. Looking first at the waveform of diagram (A), the data inversion point X in the original data, which occurs at a time point t2, is preceded by 1 Tmin period at the digital 0 state, and succeeded by 3 Tmin periods at the digital 1 state. Conversely, the data inversion point Y is preceded by 3 Tmin periods at the digital 1 state and is succeeded by one Tmin period at the digital 0 state.
Playback of an optical disk is based upon energy, and such playback operation does not include elements which are of mutually opposite kind, such as the N and S polarities of a magnetic recording and playback system. For that reason, when a lack of sharpness due to spherical aberration in the optical system arises, then as shown in diagram (B) of FIG. 3, the ends of the long code portion (3 Tmin of data) will become lengthened so that the portion of the waveform at time point t2 is shifted towards the time point t1 and the portion of the waveform at t3 is shifted towards t4. In addition, the distortion that results from coma aberration can cause even more serious effects. Diagram (C) of FIG. 3 shows a case in which coma aberration is produced which is oriented in the opposite direction to the direction of disk rotation, while diagram (D) shows a case in which coma aberration is produced which is oriented along the direction of disk rotation. It can be seen that the amount and shape of the waveform distortion of the playback signal will differ in accordance with these two types of coma aberration.
When reading data from an optical recording and playback system, e.g. from an optical disk (referred to in the following simply as a CD), there will generally be high levels of these different types of aberration in the lens and the optical system, and it is not possible to quantitatively determine the respective amounts of distortion that arise from the various types of aberration. Thus it has been almost impossible to achieve effective waveform equalization in the prior art. Taking for example the prior art waveform equalizer shown in FIG. 1, respectively different coefficient values would be required, i.e. different values of amplification factors for the amplifiers 131a to 131e, depending upon the degree of intersymbolic interference (i.e. degree of code distortion) and the causes of the distortion. Thus the coefficient values cannot be unconditionally defined, so that it has not been possible to achieve satisfactory results with the such prior art types of waveform equalizer, which have linear input/output characteristics.
In the case of the signal distortion conditions which arise in a magnetic recording and playback system, as illustrated in diagrams (D) and (E) of FIG. 2, it would be possible for an individual who is highly experienced in the characteristics of a magnetic recording and playback system and the NRZ code to make correct judgements concerning the playback signal, by examining such a static waveform diagram. That is to say, the polarity inversions always occur in pairs, so that each positive-going inversion of the playback signal should always be followed by a negative-going inversion, i.e. there should be a sequence of positive-negative, positive-negative, inversions. Hence, considering the time points t2 and t3, it can be judged that inversions occur in that portion of the waveform of diagram (D) of FIG. 2 within a short time interval, and since the period has been lengthened as a result of bit shifting in that portion, the inversion points could be correctly judged as being at the time points t2, t3, rather than at the points t1, t4 (which erroneous judgement might be made based on the results of differentiation, shown in diagram (E)). Similarly, since the playback signal waveform is positive at each of the time points t5, t6 and t7, i.e. positive-negative inversion pairs do not appear, it would be judged by an experienced individual that t6 is a data inversion point.
Furthermore, in the case of the signal distortion conditions in an optical recording and playback system that are illustrated in diagrams (B) to (D) of FIG. 3, it would be possible for an experienced individual who is very familiar with the characteristics of such an optical recording and playback system to make correct judgements of the playback signal waveform. Specifically, from the slope of the 3 Tmin data portion extending betweeen t2 and t4, it would be possible for such an individual to estimate the direction and the amount of coma aberration, and based on that knowledge, to correctly judge the transition points (t2, t3) of the playback signal.
However it is not practicable to execute real-time elimination of signal distortion that arises in a digital signal recording and playback system or transmission system, by a method which uses human experience and analysis as described above. Prior art types of waveform equalizer cannot provide satisfactory performance, and in addition the design of such a waveform equalizer (for example, to determine the amplification factors in accordance with the characteristics of a particular recording and playback system) is complex.
Recently, signal processing by neural networks has been proposed in various types of applications. A neural network consists of a plurality of neuron units, each having a non-linear input/output characteristic, and interconnected by linking elements which have respective mutually independent weighting coefficients. The weighting coefficients can be altered by a learning operation, which involves comparing an output value produced from the neural network (while a specific combination of input values are being inputted to the neural network) with a desired value (referred to as a teaching value), and modifying the values of the weighting coefficients such as to bring the output value from the neural network closer to the teaching value, by using a learning algorithm. The learning process is successively repeated for a number of different teaching values and corresponding input value combinations. The operation of a neural network is generally implemented by simulation using a computer. As a result, it has not been possible to achieve a sufficiently high performance with a neural network (due to the limited processing speed capabilities of the usual types of computer) to execute real-time signal processing for such a waveform equalizer type of application. Moreover, it is difficult to realize neuron units as practical hardware circuits which have non-linear input/output characteristics.
Due to the above factors, it has not been considered practicable to use a neural network to learn the characteristics of a magnetic recording and playback system or an optical recording and playback system and to thereby execute real-time equalization of a distorted digital signal that is produced from a transmission or playback system.